In the field of oil well development, directional measurements are made to determine, for example, the distance between formation boundaries and a drilling apparatus, orientation of the formation boundaries with respect to the drilling apparatus, and to facilitate proactive well placement and formation evaluation. Directional measurements are often made from information gathered by electromagnetic LWD (Logging While Drilling) tools, which may employ antennas, disposed in the drilling apparatus. These tools operate over time and at different frequencies to provide multi-spacing and multi-frequency measurements. The received signals depend on a number of variables, including the transmitter-to-receiver spacing, frequency, azimuthal angle of the receiver(s), and the orientation angle of the formation relative to the receivers.
When the drilling apparatus, and thus the tools disposed in the drilling string, is rotating, the measured signal for an axial transmitter and tilted receiver is expressed as: V=a0+a1 cos(φ−φ), where V is received voltage, a0 is a zeroth harmonic coefficient, a1 is a first harmonic coefficient, φ is an azimuth angle of said receiver, and φ is an orientation angle of a formation relative to the receiver. The orientation angle φ is, for a given location of the receiver, the angle between the normal to the formation and a reference line in a plane perpendicular to the tool axis. A ratio of first and zeroth harmonic coefficients can be used to estimate the distance between the logging tool and the bed boundary. This is the basis of directional measurement. The signals measured at different receiver azimuthal angles are used in a fitting algorithm, as known in the art, to determine the zeroth and first harmonic coefficients and the orientation angle of the formation. This is possible as multiple measurements made during rotation provide sufficient data to apply the fitting algorithm. However, when the drill string is not rotating, the measurements are insufficient to use the fitting algorithm. According to the known art, in such case the coefficients and orientation angle of the formation, and therefore the directional measurements, cannot be determined. As a result, directional measurements can only be made when the drilling apparatus is rotating.
According to the known art, information obtained from directional measurements is used to steer a drilling apparatus. For instance, directional measurements are used to guide a rotary steerable system since that system rotates continuously. As such, directional measurements can be continuously made throughout the drilling process. However, when mud motors or similar mechanisms are used to drill the well, the direction of the drilling apparatus is changed by pushing or sliding the apparatus in a different direction. In this case, other than the drill bit, the drill string does not rotate as it is used in a new direction. Therefore, directional measurements cannot be taken during this time. Desirably, one would be able to determine coefficients used to construct directional measurements even when the drilling apparatus is not rotating.
There are known methods for obtaining directional measurements while the drilling apparatus is not rotating. Such methods involve making what are commonly referred to as tri-axial measurements. However, the employment of tri-axial measurements is burdensome, particularly in view of the present invention. For instance, making tri-axial measurements requires that additional sensors be placed on the drilling apparatus; also, the sensors must be synchronized with one another to obtain sufficiently accurate measurements. As such, the employment of tri-axial measurements increases the complexity of the machinery and requires additional steps for obtaining directional measurements.
In view of the above, a need exists for determining the coefficients necessary to construct directional measurements in an efficient and computationally straightforward manner, even when the drilling is not rotating.